The Nicaraguan government has informed the United States that it will not permit $5.1 million in aid to go to private groups in that country, partly on grounds that the money is intended to undermine the Sandinista regime.

Nicaragua's decision, made known by its embassy here, is likely to bring new issues of contention to the already tense relations between the two countries.

The decision reportedly was a surprise to the State Department, where a letter renouncing the aid offer was said to be under "careful study."

According to a spokesman, there had been no objection by the Nicaraguan government in previous years to the offer and delivery of similar aid, including $8.5 million in support for the Nicaraguan private sector in fiscal 1981.

Managua's objections apparently flowed in part from U.S. statements before Congress characterizing the aid as "a symbol of political and moral support" for Nicaraguans who "desire to be free."

Such a statement was made by Otto J. Reich, assistant administrator for Latin America of the Agency for International Development, in testimony before a House Appropriations subcommittee on June 23.

Reich also said AID dollars for this program would be channeled so that they did not pass through the Central Bank of Nicaragua. AID officials said yesterday the same procedure had been used in the past.

The $5.1 million for fiscal 1982 was to be directed to 16 private organizations, including the Nicaraguan Development Foundation, the Private Enterprise Council, the Associations of Cattlemen, Coffee Growers and Rice Producers, the American School and the Roman Catholic Church.

Edmundo Jarquin, executive director of the International Fund for Reconstruction, Nicaragua's aid-receiving agency, informed AID by letter Monday that "it is impossible to accept the AID funds" under existing circumstances, according to a Nicaraguan press statement released here.

The statement charged that "Nicaragua has suffered numerous economic aggressions from the present U.S. administration," including failure to disburse previously promised government-to-government aid, and U.S. opposition to loans to Nicaragua by multinational development banks.

Managua also charged in the statement that the planned aid to the private-sector organizations is "inconsistent with the country's priorities" and discriminates against the Nicaraguan government. President Reagan ordered government-to-government aid stopped in April, 1981, on grounds that the Nicaraguan regime continued to support insurgents in nearby El Salvador.

"Finally, U.S. congressional hearings revealed that the agreements with the private sector have political motivations designed to promote resistance and destabilize the revolutionary government," the statement said.

State Department officials said the last paragraph of Jarquin's letter spoke of Nicaragua's willingness to have further discussions about bilateral aid programs. For this reason, one official called the Nicaraguan position "a rejection with a window left open."

The Nicaraguan announcement came as administration officials testified before the Senate Foreign Relations Committee in support of continued U.S. military aid to El Salvador.

The administration last week certified, as required by law, that enough progress toward human rights and reforms is being made in that country to continue an $81 million U.S. military assistance program in the current year.